We decided that as green and yellow jelly babies close in colour and difficult to distinguish that we would group them together
Grass
Black
Green & Yellow
Orange
red
5
13
2
0
5
13
1
1
6
9
4
1
Observed
16
35
7
2
Expected
15
15
15
15
O-E
1
10
-8
-13
(O-E)2
1
100
64
169
(O-E)2/E
0.066667
6.666666667
4.266667
11.26667
22.26667
d.f
(4-1)x(3-1) = 6
Reject null hypothesis because the value is greater then 12.59 which is the 5% critical value (see table),
Shrub
Black
Green & Yellow
Orange
red
3
16
0
1
6
10
0
4
3
15
0
2
Observed
12
41
0
7
Excepted
15
15
15
15
O-E
-3
26
-15
-8
(O-E)2
9
676
225
64
(O-E)2/E
0.6
45.06666667
15
4.266667
64.93333
d.f
(4-1)x(3-1) = 6
(d.f. = degrees of freedom)
Shrub
Black
Green & Yellow
red
3
16
1
6
10
4
3
15
2
Observed
12
41
7
Excepted
15
15
15
O-E
-3
26
-8
(O-E)2
9
676
64
(O-E)2/E
0.6
45.06666667
4.266667
49.93333
d.f
(4-1)x(3-1) = 6
In the table above we see that even when the orange snails are omitted from the test (as there were 0 of them) the result is still significant.
Both tests yielded a significant result (rejection of the null hypothesis), this means that we would expect to see deviations from the expected value as large as this less than 5% of the time if the null hypothesis were true. This implies that it is likely that there is a significant difference in the type of snails that live in grassy and shrub areas. The large present of the green/yellow may imply that they are the best adapted snail either environment (grass and shrub land)
Degrees of Freedom (df)
Probability (p)
0.95
0.90
0.80
0.70
0.50
0.30
0.20
0.10
0.05
0.01
0.001
1
0.004
0.02
0.06
0.15
0.46
1.07
1.64
2.71
3.84
6.64
10.83
2
0.10
0.21
0.45
0.71
1.39
2.41
3.22
4.60
5.99
9.21
13.82
3
0.35
0.58
1.01
1.42
2.37
3.66
4.64
6.25
7.82
11.34
16.27
4
0.71
1.06
1.65
2.20
3.36
4.88
5.99
7.78
9.49
13.28
18.47
5
1.14
1.61
2.34
3.00
4.35
6.06
7.29
9.24
11.07
15.09
20.52
6
1.63
2.20
3.07
3.83
5.35
7.23
8.56
10.64
12.59
16.81
22.46
7
2.17
2.83
3.82
4.67
6.35
8.38
9.80
12.02
14.07
18.48
24.32
8
2.73
3.49
4.59
5.53
7.34
9.52
11.03
13.36
15.51
20.09
26.12
9
3.32
4.17
5.38
6.39
8.34
10.66
12.24
14.68
16.92
21.67
27.88
10
3.94
4.86
6.18
7.27
9.34
11.78
13.44
15.99
18.31
23.21
29.59
Nonsignificant
Significant
Source: R.A. Fisher and F. Yates, Statistical Tables for Biological Agricultural and Medical Research, 6th ed., Table IV, Oliver & Boyd, Ltd., Edinburgh, by permission of the authors and publishers.
1
Black Green Orange Yellow
5 8 2 5
2
Black Green Red Yellow
3 5 1 11
3
Black Green Orange Red Yellow
5 6 1 1 7
4
Black Green Red Yellow
6 4 4 6
5
Black Green Orange Red Yellow
6 2 4 1 7
6
Black Green Red Yellow
3 8 2 7
We decided that as green and yellow jelly babies close in colour and difficult to distinguish that we would group them together
In the table above we see that even when the orange snails are omitted from the test (as there were 0 of them) the result is still significant.
Both tests yielded a significant result (rejection of the null hypothesis), this means that we would expect to see deviations from the expected value as large as this less than 5% of the time if the null hypothesis were true. This implies that it is likely that there is a significant difference in the type of snails that live in grassy and shrub areas. The large present of the green/yellow may imply that they are the best adapted snail either environment (grass and shrub land)
Freedom
(df)
Source: R.A. Fisher and F. Yates, Statistical Tables for Biological Agricultural and Medical Research, 6th ed., Table IV, Oliver & Boyd, Ltd., Edinburgh, by permission of the authors and publishers.